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" If " |{:(x^(2)+x,,x+1,,x-2),(2x^(2)+3...

`" If " |{:(x^(2)+x,,x+1,,x-2),(2x^(2)+3x-1,,3x,,3x-3),(x^(2)+2x+3,,2x-1,,2x-1):}|=xA +B` then

A

12

B

18

C

24

D

30

Text Solution

Verified by Experts

The correct Answer is:
C
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Without expanding a determinant at any stage, show that |{:(x^(2)+x, x+1, x+2),(2x^(2) +3x-1, 3x, 3x-3),(x^(2) +2x+3, 2x-1, 2x-1):}|=xA+B where A and B are determinants of order 3 not involving x.

If |(x^2+x,x+1,x-2),(2x^2+3x-1,3x,3x-3),(x^2+2x+3,2x-1,2x-1)|=ax-12 then 'a' is equal to (1) 12 (2) 24 (3) -12 (4) -24

y=|(x^2+x, x+1, x-2),(2x^2+3x+1, 3x, 3x-3),(x^2+3x+2, 2x-1, 2x-1)| represents (A) a straight line (B) a circle (C) a parabola (D) none of these

x ^ (2) + 2x + 3x = 1

If |{:(x^(2) +x , 3x - 1 , -x + 3),(2x +1 , 2 + x^(2) , x^(3) - 3),(x - 3, x^(2) + 4, 3x):}| = a_(0) + a_(1) x + a_(2) x^(2) + .... + x_(7) x^(7), then the value of a_(0) is

(x^(2)-x)-(1)/(2)(x-3+3x^(2))

[[3x^(2),3x,1x^(2)+2x,2x+1,12x+1,x+2,1]]=(x-1)^(3)

im_(-)>1[(x-2)/(x^(2)-x)-(1)/(x^(3)-3x^(2)+2x)]

If f(x)=|{:(1,x,x+1),(2x,x(x-1),(x+1)x),(3x(x-1),x(x-1)(x-2),(x+1)x(x-1)):}| then

lim_(xrarr1) [(x-2)/(x^(2)-x)-(1)/(x^(3)-3x^(2)+2x)]

MCGROW HILL PUBLICATION-DETERMINANTS-QUESTIONS FROM PREVIOUS YEARS B-ARCHITECTURE ENTRANCE EXAMINATION PAPERS
  1. " If " |{:(x^(2)+x,,x+1,,x-2),(2x^(2)+3x-1,,3x,,3x-3),(x^(2)+2x+3,,2x...

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  2. If the system of equations x+y+z=0 ax+by+z=0 bx+y+z=0 has a no...

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  3. The system of linear equations (lamda+3)x+(lamda+2)y+z=0 3x+(lamda...

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  4. If Delta(k)=|(2(3^(k-1)),3(4^(k-1)),4(5^(k)-1)),(alpha, beta, gamma)...

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  5. Let P=[a("ij")] be a 3xx3 matrix and let Q=[b("ij")], where b("ij")=2^...

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  6. Let Delta(r)=|(2^(r-1),2(3^(r-1)),4(5^(r-1))),(alpha, beta, gamma),(2^...

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  7. If x(1),x(2),x(3),……………..x(13) are in A.P. then the value of |(e^(x(...

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  8. Find the value of determinat |{:(sqrt(13)+sqrt(3),2sqrt(5),sqrt(5)),(...

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  9. If the system of linear equations x+2ay +az =0,x+3by+bz =0 and x+4cy ...

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  10. In a Delta ABC " if " |(1,a,b),(1,c,a),(1,b,c)| =0, then sin^(2) A + s...

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  11. The system of lienar equations x-y+z=1 x+y-z=3 x-4y+4z=alpha has

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  12. For all values of theta in(0,pi/2), the determinant of the matrix [(...

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  13. Les S the set of all real values of a for which the following system o...

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  14. |(2x,xy-xz,y),(2x+z+1,xy-xz+yz-z^2,1+y),(3x+1,2xy-2xz,1+y)| is equal t...

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  15. Let S be the set of all real values of lamda for which the system of l...

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  16. Ifthe equations a(y +z) =x,b(z+x) = y, c (x + y) = z have nontrivial...

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  17. The value of a for whch the sytem of equations x+ay+z=1 ax+y+z=1 ...

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  18. If the system of linear equations x+4y-3z=2 2x+7y-4z=alpha -x-5y...

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  19. The number of solutions of the equation 3x-y-z=0 -3x+2y+z=0 -3x+...

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